A general convergence principle in nonlinear functional analysis

DOI10.1016/0362-546X(80)90006-1zbMath0454.65043OpenAlexW2053113508MaRDI QIDQ3902410

Ronald E. jun. Bruck, Simeon Reich

Publication date: 1980

Published in: Nonlinear Analysis: Theory, Methods & Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0362-546x(80)90006-1

zbMATH Keywords

accretive operatorweak convergenceNewton's methodminimization problemeigenvalue problemsubdifferentialadmissible pairconvergence conditionduality mapnearest point mapnonlinear nonexpansive semigroupexplicit and implicit iterative schemesgeneral convergence principle

Mathematics Subject Classification ID

Semigroups of nonlinear operators (47H20) Nonlinear accretive operators, dissipative operators, etc. (47H06) Iterative procedures involving nonlinear operators (47J25) Geometry and structure of normed linear spaces (46B20) Nonlinear spectral theory, nonlinear eigenvalue problems (47J10) Numerical solutions to equations with nonlinear operators (65J15)

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Cites Work

• Weak convergence theorems for nonexpansive mappings in Banach spaces
• Asymptotic convergence of nonlinear contraction semigroups in Hilbert space
• Solution of eigenvalue problems in Hilbert spaces by a gradient method
• An iterative solution of a variational inequality for certain monotone operators in Hilbert space
• An iterative procedure for constructing zeros of accretive sets in Banach spaces
• Unnamed Item